Dimensions of Torque

Dimensional Formula of Torque

The dimensional formula of torque is given by,

M1 L2 T-2

Where,

  • M = Mass
  • L = Length
  • T = Time

Derivation

Torque (T) = Moment of Inertia × Angular Acceleration . . . . (1)

Since, Moment of Inertia (M.O.I) = Radius of Gyration2 × Mass

∴ The dimensional formula of Moment of Inertia = M1 L2 T0 . . . (2)

And, Angular Acceleration = Angular velocity × Time-1

∴ The dimensional formula of Angular Acceleration = M0 L0 T-2 . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Torque = Moment of Inertia × Angular Acceleration

Or, I = [M1 L2 T0] × [M0 L0 T-2] = [M L2 T-2].

Therefore, the torque is dimensionally represented as [M L2 T-2].

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